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+// Copyright (c) 2015 John Maddock
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+#ifndef BOOST_MATH_ELLINT_RG_HPP
+#define BOOST_MATH_ELLINT_RG_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/tools/config.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/special_functions/ellint_rd.hpp>
+#include <boost/math/special_functions/ellint_rf.hpp>
+#include <boost/math/special_functions/pow.hpp>
+
+namespace boost { namespace math { namespace detail{
+
+ template <typename T, typename Policy>
+ T ellint_rg_imp(T x, T y, T z, const Policy& pol)
+ {
+ BOOST_MATH_STD_USING
+ static const char* function = "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)";
+
+ if(x < 0 || y < 0 || z < 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "domain error, all arguments must be non-negative, "
+ "only sensible result is %1%.",
+ std::numeric_limits<T>::quiet_NaN(), pol);
+ }
+ //
+ // Function is symmetric in x, y and z, but we require
+ // (x - z)(y - z) >= 0 to avoid cancellation error in the result
+ // which implies (for example) x >= z >= y
+ //
+ using std::swap;
+ if(x < y)
+ swap(x, y);
+ if(x < z)
+ swap(x, z);
+ if(y > z)
+ swap(y, z);
+
+ BOOST_ASSERT(x >= z);
+ BOOST_ASSERT(z >= y);
+ //
+ // Special cases from http://dlmf.nist.gov/19.20#ii
+ //
+ if(x == z)
+ {
+ if(y == z)
+ {
+ // x = y = z
+ // This also works for x = y = z = 0 presumably.
+ return sqrt(x);
+ }
+ else if(y == 0)
+ {
+ // x = y, z = 0
+ return constants::pi<T>() * sqrt(x) / 4;
+ }
+ else
+ {
+ // x = z, y != 0
+ swap(x, y);
+ return (x == 0) ? T(sqrt(z) / 2) : T((z * ellint_rc_imp(x, z, pol) + sqrt(x)) / 2);
+ }
+ }
+ else if(y == z)
+ {
+ if(x == 0)
+ return constants::pi<T>() * sqrt(y) / 4;
+ else
+ return (y == 0) ? T(sqrt(x) / 2) : T((y * ellint_rc_imp(x, y, pol) + sqrt(x)) / 2);
+ }
+ else if(y == 0)
+ {
+ swap(y, z);
+ //
+ // Special handling for common case, from
+ // Numerical Computation of Real or Complex Elliptic Integrals, eq.46
+ //
+ T xn = sqrt(x);
+ T yn = sqrt(y);
+ T x0 = xn;
+ T y0 = yn;
+ T sum = 0;
+ T sum_pow = 0.25f;
+
+ while(fabs(xn - yn) >= 2.7 * tools::root_epsilon<T>() * fabs(xn))
+ {
+ T t = sqrt(xn * yn);
+ xn = (xn + yn) / 2;
+ yn = t;
+ sum_pow *= 2;
+ sum += sum_pow * boost::math::pow<2>(xn - yn);
+ }
+ T RF = constants::pi<T>() / (xn + yn);
+ return ((boost::math::pow<2>((x0 + y0) / 2) - sum) * RF) / 2;
+ }
+ return (z * ellint_rf_imp(x, y, z, pol)
+ - (x - z) * (y - z) * ellint_rd_imp(x, y, z, pol) / 3
+ + sqrt(x * y / z)) / 2;
+ }
+
+} // namespace detail
+
+template <class T1, class T2, class T3, class Policy>
+inline typename tools::promote_args<T1, T2, T3>::type
+ ellint_rg(T1 x, T2 y, T3 z, const Policy& pol)
+{
+ typedef typename tools::promote_args<T1, T2, T3>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ return policies::checked_narrowing_cast<result_type, Policy>(
+ detail::ellint_rg_imp(
+ static_cast<value_type>(x),
+ static_cast<value_type>(y),
+ static_cast<value_type>(z), pol), "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)");
+}
+
+template <class T1, class T2, class T3>
+inline typename tools::promote_args<T1, T2, T3>::type
+ ellint_rg(T1 x, T2 y, T3 z)
+{
+ return ellint_rg(x, y, z, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ELLINT_RG_HPP
+